Many kinds of exercise devices have been used on bicycles and other pedal-operated equipment to artificially increase resistance to pedaling whereby a rider will have to exert greater force upon the bicycle pedals in order to turn them. Some such devices are found in so-called “stationary” bicycles which are designed to be used in a gymnasium or other enclosed area, and which serve the sole purpose of providing resistance to a pedaling movement. Other exercise devices have been designed as stationary platforms for standard bicycles that can be placed upon the platform to provide resistance to pedaling. Because stationary bikes and standard bicycles placed upon a stationary platform are not mobile, and are used within a controlled physical space, the friction generating mechanisms can be as large, heavy, or intricate as may be required to provide the necessary resistance to motion. However, bicycles are primarily used for traversing terrain, and many riders enjoy the freedom of being able to cover distances on a bicycle while also obtaining exercise. For such riders, a suitable exercise device must be mounted upon the bicycle and must be operable by a rider under varying conditions of speed and terrain. For a bicycle-mounted exercise device, factors such as weight, simplicity of operation, ruggedness, and efficiency in dissipating heat that is generated through the friction of restraining the circular motion of the bicycle driving wheel take on added importance.